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WASHINGTON (CNN) -- The insurgency in Iraq is "in the last throes," Vice President Dick Cheney says, and he predicts that the fighting will end before the Bush administration leaves office.

In a wide-ranging interview Monday on CNN's "Larry King Live," Cheney cited the recent push by Iraqi forces to crack down on insurgent activity in Baghdad and reports that the most-wanted terrorist leader, Abu Musab al-Zarqawi, had been wounded.

The vice president said he expected the war would end during President Bush's second term, which ends in 2009.

"I think we may well have some kind of presence there over a period of time," Cheney said. "The level of activity that we see today from a military standpoint, I think, will clearly decline. I think they're in the last throes, if you will, of the insurgency."

Cheney was among the Bush administration's most forceful advocates of the U.S.-led invasion in 2003. Bush, Cheney and other top officials said war was necessary because Iraq was maintaining illicit stockpiles of chemical and biological weapons and concealing a nuclear weapons program from U.N. weapons inspectors and could have provided those weapons to terrorists.

No banned weapons were found after U.S. troops deposed Iraqi leader Saddam Hussein's government, though U.S. inspectors said Iraq was concealing some weapons-related research from the United Nations.

Nevertheless, Cheney said he was "absolutely convinced we did the right thing in Iraq." He said the United States was making "major progress" in Iraq, where a transitional government took power in April and was working on drafting a new constitution.

"America will be safer in the long run when Iraq, and Afghanistan as well, are no longer safe havens for terrorists or places where people can gather and plan and organize attacks against the United States," he said.

Saddam's government collapsed in just three weeks, but a persistent guerrilla campaign against U.S. troops and the fledgling Iraqi government has lasted more than two years. The number of U.S. troops killed in the conflict now tops 1,650, and estimates of the number of Iraqi deaths range into the tens of thousands.

Since the conflict, the Jordanian-born Islamic militant al-Zarqawi has been blamed for dozens of bombings that have left hundreds of people dead. Reports emerged last week that he had been wounded in combat -- but in an audiotaped statement released Monday on militant Islamic Web sites, a man claiming to be al-Zarqawi said the injury was minor. (Full story)